What is the derivative of (\sqrt[4]{x}^{ln(x)}) ?

The derivative of (\sqrt[4]{x}^{ln(x)}) is (e^{(ln^2(x))/4}ln(x))/(2x)

What is the first derivative of (\sqrt[4]{x}^{ln(x)}) ?

The first derivative of (\sqrt[4]{x}^{ln(x)}) is (e^{(ln^2(x))/4}ln(x))/(2x)

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\frac{e ^{\frac{l n ^{2} ( x )}{4}} ln ( x )}{2 x}

Solution steps

Apply exponent rule:

a^{b} = e^{b l n (a)}

Apply the chain rule:

Simplify

= \frac{e ^{\frac{l n ^{2} ( x )}{4}} ln ( x )}{2 x}

\frac{d x}{d t} = 2 x + t + 1

25 y^{^{''}} - 30 y^{^{'}} + 9 y = 0

\int \frac{1}{2 t ^{2} + 3 t + 1} d t

y = \frac{x}{2 x - 4}

\frac{d}{d x} (\frac{r ( x )}{x})

What is the derivative of (\sqrt[4]{x}^{ln(x)}) ?
The derivative of (\sqrt[4]{x}^{ln(x)}) is (e^{(ln^2(x))/4}ln(x))/(2x)
What is the first derivative of (\sqrt[4]{x}^{ln(x)}) ?
The first derivative of (\sqrt[4]{x}^{ln(x)}) is (e^{(ln^2(x))/4}ln(x))/(2x)